4w⁹ -2w⁹
= (4-2)w⁹ . . . . . distributive property, or "collecting terms"
= 2w⁹
_____
In plain text, a caret (^) is used to identify an exponent. w⁹ = w^9. If the exponent has any arithmetic, you need parentheses around it. w^(8+1)
Answer:
a)B)9π
b)G)16π in²
Step-by-step explanation:
according to the question
as we know
C/d=π
C=dπ
Therefore
C=9π
Answer:
a) positive direction: t < 2s & t>6s ; negative direction: 2s < t < 6s
b) 7 m
c) 71 m
Step-by-step explanation:
Given:
v(t) = 3t^2 -24t +36 [0 , 7]
Find:
a) The value of time when particle is moving in positive direction:
The change in direction of the particle can be determined by v(t) > 0
Hence,
0 < 3t^2 -24t +36
0 < t^2 - 8t + 12
0 < (t - 2)*(t - 6)
t < 2s , t > 6s
The particle travels in positive direction in the interval t < 2s and t > 6s , While it travels in negative direction when 2s < t < 6s.
b) The displacement ds over the given interval [ 0 , 7 ]
ds = integral (v(t)).dt
ds = t^3 -12t^2 +36t
ds = 7^3 -12*7^2 +36*7
ds = 7 m
c) Total distance traveled in the interval:
Total distance= ds(0-2) + ds(2-6) + ds(6-7)
D = 2*(2^3 -12*2^2 +36*2) - 2*(6^3 -12*6^2 +36*6) + 7
D = 2*32 - 2*0 + 7
D = 71 m
<span>
<u><em>Answer:</em></u>8.4 square units
<u><em>Explanation:</em></u><u>The area of the triangle can be calculated using two sides and an included angle as follows:</u>
area = 0.5 * 1st side * 2nd side * sin(angle included between them)
............> This is shown in the attached image
<u>In the given triangle, we have:</u>
the two sides 2*</span>√2<span> and 6 units
the angle included between them is 80</span>°<span>
Therefore, we can apply the above rule to get the area as follows:
area = 0.5 * 2</span>√2 <span>*6* sin(80</span>°<span>)
area = 8.35 which is approximately 8.4 square units
Hope this helps :)</span>